Extracorporeal blood pumps used today in conjunction with surgical procedures, dialysis, blood oxygenation, etc. are almost exclusively in the form of peristaltic roller pumps. Peristaltic pumps when used in the present context are encumbered with a number of serious drawbacks, however. For example, when pumping blood with the aid of a roller operated peristaltic pump it is difficult to prevent damage to blood corpuscles in the pumped blood, when the hose through which the blood is conducted is subjected to the pressure of the rollers. Thus, it is difficult to avoid part of the blood corpuscles present from being crushed and destroyed as the hose is compressed by the rollers acting thereon. Even though the compression rollers do not close the hose completely, but leave a narrow through passage, the flow velocities occuring in this narrow passage are so high as to cause damage to the blood corpuscles in the blood pumped therethrough. Another serious problem is encountered with the use of such pumps when the flow of blood to the inlet side of the pump radically diminishes or ceases completely, for example as a result of a blockage at the end of the catheter connecting the pump to a blood vessel. Such blockages are liable to occur with relative ease, for example as a result of abutment of the catheter orifice with the wall of the aforesaid blood vessel. In cases such as these a peristaltic pump will continue to carry out a pumping action, and in doing so will create on the inlet side of the pump subpressures of such magnitude as to cause serious injury to the patient connected to the pump. In addition it is difficult to adapt the flow and pressure characteristics of a peristaltic pump to what can be considered suitable characteristics from a physiological aspect. The use of especially designed centrifugal pumps as extracorporeal blood pumps has also been tried to some extent. Such pumps expose the pumped blood to extremely high shear forces, which are liable to damage the blood corpuscles. In order to achieve high pressures, it is necessary to employ extremely high rotational velocities.